A corresponding hybrid module is known from WO 2014/026685 A1. Said document presents a hybrid module for a drivetrain of a motor vehicle, in which an electric machine is arranged between an internal combustion engine and a transmission. The hybrid module has a rotor of the electric machine and has a separating clutch arranged within the rotor, which separating clutch has a pressure plate and a counterplate. Furthermore, in conjunction with such hybrid modules, there is generally provided in the drivetrain a clutch device with at least one friction clutch, which in turn has a pressure plate and a counterplate.